Related papers: Fisher information for quasi-one-dimensional hydro…
The Fisher-Shannon information and a statistical measure of complexity are calculated in the position and momentum spaces for the wave functions of the quantum isotropic harmonic oscillator. We show that these magnitudes are independent of…
We find approximate analytical presentation of the solutions $\Psi(r_1, r_2, r_{12})$ of Schr\"odinger equation for two-electron system bound by the nucleus, in the space region $r_{1,2}=0$ and $r_{12}=0$ that are of great importance for a…
Position and momentum representations of a wavefunction $\psi(x)$ and $\phi(p)$, respectively are physically equivalent yet mathematically in a given case one may be easier or more transparent than the other. This disparity may be so much…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure…
We show that the weak equivalence principle (WEP) is violated for a quantum particle in a gravitational wave (GW) background, in the sense that extra mass information can be extracted in the presence of the GW. We quantify the degree of…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
A new description for highly nonlinear potential water waves is suggested, where weak 3D effects are included as small corrections to exact 2D equations written in conformal variables. Contrary to the traditional approach, a small parameter…
Quantum mechanics gives a new breakthrough to the field of parameter estimation. In the realm of quantum metrology, the precision of parameter estimation is limited by the quantum Fisher information. We introduce the measures of partial…
Wave functions of a new functional kind have been proposed for Helium-like atoms in this work . These functions explicitly depend on interelectronic and hyperspherical coordinates. The best ground state energy for the Helium atom $…
The Fourier component of the potential energy of interaction of an atom with an atom is represented as a polynomial of the fourth degree from the atomic form factor. A numerical calculation was performed for the atomic form factor in the…
Wigner phase space quasi-probability distribution function is a Fourier transform related to a given quantum mechanical wave function. It is shown that for the wave functions of type $\psi (q)=e^{-aq^2}\phi (q)$, the Wigner function can be…
We present a method to estimate the quantum Fisher information (QFI) of many-body quantum states in the presence of decoherence, where its direct evaluation requires the full spectral resolution of the density matrix. We show that, for…
Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the…
This note reviews a recent contribution about the Fisher information for the space-homogeneous Boltzmann equation by L. Silvestre, C. Villani and the author (arXiv, 2024). This classical functional from information theory is shown to be…
We solve the stationary Schr\"odinger equation for a particle confined to a 3D spherical wedge -- the region $\{(r,\theta,\phi): 0 \leq r \leq R,\, 0 \leq \theta \leq \pi,\, 0 \leq \phi \leq \Phi\}$ with Dirichlet BCs on all surfaces. This…
The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich…
Fisher information (I) is investigated for confined hydrogen atom (CHA)-like systems in conjugate $r$ and $p$ spaces. A comparative study between CHA and free H atom (with respect to $I$) is pursued. In many aspects, inferences in CHA are…
A rigorous characterization of the information content of any highest-spin three-fermion wave function is presented. It is based upon a formal decomposition of the wave function into a finite set of fixed invariants, called shapes, whose…
A many-body wave function is approximated by a product of two functions: the wave function $\phi$ depending on the particle coordinates and the function $\chi$ depending only on the value of interparticle interaction potential. For the…